Remark: The above approximations provide closed form expressions for \(\theta _r\)  and are valid when \(N\)  is large [1]}.
The first two approximations have SINRs that are obtained by applying the theory of deterministic equivalents to only the norms of the channels, and yields an SINR that is affected only by the randomness in the multi-user interference components.
This is supported by the fact that the interference components converge to their deterministic equivalents slower than the norms converge to their deterministic equivalents [1]}.
The deterministic approximation follows directly from Lemma REF , where the SINR is a deterministic quantity, and hence \(\theta _r\)  is a binary function of \(r\) .
With finite number of antennas, due to small scale fading, the SINR of the users vary around this approximate SINR.
These variations affect the value of \(\theta _r\) , and are not captured by the deterministic approximation, even though we obtain simple closed form expressions for it.
As a consequence, the throughput computed using the deterministic approximation can be far from the actual throughput in certain regimes and close to the actual throughput in other regimes, as will be seen in Sec. REF .
